Integration can be interpreted as the area that lies between a curve and the xaxis, signed according to whether this area is above or below the axis. Some integrals cannot be computed directly, using symbolic means, and instead have to be approximated numerically. One classic example of this is the Gaussian error function, which was mentioned in the Basic mathematical functions section in Chapter1, Basic Packages, Functions, and Concepts. This is defined by the formula
and the integral that appears here cannot be evaluated symbolically.
In this recipe, we will see how to use the numerical integration routines in the SciPy package to compute the integral of a function.
Getting ready
We use the scipy.integratemodule, which contains several routines for computing numerical integrals. We import this module as follows:
from scipy import integrate